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Answers to HW 1
1. Sample space is composed of 52 elements such as
{A,2,3,4,5,6,7,8,9,10,J,Q,K} associated with 4 different suits. For
instance, the probability of event {A,J} is assigned as p(A,J) =
8/52=2/13
2. 1/3; 2/3; ba, if
ba
≥
.
3. p(LU)=0, P(CU)=
1
7
12
12
31
12
7
=
+
4. P(UC)=
1
1
12
11
3
12
6
=
+
, P(MC)=
1
2
6
3
12
6
=
+
5. The expected payoff of player 2 is
1
2
2
1
2
0
(
2)
( 2
2)
1
33
5
5
5
3
55
5
+
++
+
=
.
6. Each 1,2,4,5 remaining in the urn is equally likely to be drawn with a
1/4 chance.
7.
Proportion Duck =
1
3
34 35
2
0
.65
⋅+⋅= =
P(RoundLamb)=
22
35
16
21
22 11
35 34
.76
⋅
==
⋅+⋅
P(BoneDuck)=
3
1
34
5
13
.38
⋅
8. (i) just one positive test result.
(
)
( 
) (
)
0.95 0.05
(
)
0.250
( )
( 
) (
)
( ~
) (~
)
0.95 0.05
0.15 0.95
p cont
p
cont p cont
p cont
p
p
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 Spring '11
 econ

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